These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 23.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0,lambda1} {lambda2,lambda1+lambda2}
These pure modular group Hurwitz classes each contain only
finitely many Thurston equivalence classes.
However, this modular group Hurwitz class contains
infinitely many Thurston equivalence classes.
The number of pure modular group Hurwitz classes
in this modular group Hurwitz class is 10.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/23, 1/1, 3/1, 5/1, 7/1, 9/1, 11/1, 13/1, 15/1, 17/1, 19/1, 21/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.049587)
( 0.050792,infinity)
The half-space computation does not determine rationality.
EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION
INTERVAL COMPUTED FOR HST OR EXTENDED HST
(0.049440,0.049773) 7/141 HST
(0.049768,0.049777) 11/221 HST
(0.049665,0.049850) 12/241 HST
(0.049798,0.049897) 17/341 HST
(0.049868,0.049927) 25/501 HST
(0.049815,0.050000) 35/701 HST
(0.049976,0.050022) 1/20 EXTENDED HST
(0.050000,0.050239) 11/219 HST
(0.050233,0.050243) 21/418 HST
(0.050243,0.050244) 444/8837 HST
(0.050243,0.050245) 72/1433 HST
(0.050245,0.050256) 10/199 HST
(0.050255,0.050257) 108/2149 HST
(0.050256,0.050259) 39/776 HST
(0.050255,0.050263) 126/2507 HST
(0.050259,0.050261) 29/577 HST
(0.050262,0.050268) 19/378 HST
(0.050267,0.050269) 75/1492 HST
(0.050269,0.050270) 28/557 HST
(0.050265,0.050275) 65/1293 HST
(0.050271,0.050285) 9/179 HST
(0.050280,0.050289) 97/1929 HST
(0.050286,0.050289) 35/696 HST
(0.050288,0.050291) 113/2247 HST
(0.050289,0.050291) 26/517 HST
(0.050290,0.050293) 69/1372 HST
(0.050292,0.050300) 17/338 HST
(0.050299,0.050300) 193/3837 HST
(0.050300,0.050305) 25/497 HST
(0.050300,0.050313) 41/815 HST
(0.050308,0.050325) 8/159 HST
(0.050317,0.050343) 23/457 HST
(0.050335,0.050406) 7/139 HST
(0.050361,0.050497) 149/2956 HST
(0.050406,0.050805) 5/99 HST
(0.050560,0.050791) 4/79 HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 3 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-20/1 1 23 Yes Yes No No
0/1 1 23 Yes Yes No No
-2206/111 1 23 Yes Yes No No
NUMBER OF EQUATORS FOUND: 3 3 0 0
The fixed point finder is unable to determine whether
there are any more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 993
Here is their union. There are no more slope function fixed points
whose negative reciprocals lie in any of the following intervals.
EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION
(-infinity,0.049773)
( 0.049773,0.050681)
( 0.050681,infinity)
NONTRIVIAL CYCLES
-159/8 -> -179/9 -> -159/8
The slope function maps every slope to a slope:
no slope maps to the nonslope.
The slope function orbit of every slope p/q with |p| <= 50
and |q| <= 50 ends in one of the above cycles.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=<1,a*b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
"b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)",
"c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
"d=<1,1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c>(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)",
"b=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)",
"c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)",
"d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)",
"b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
"c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)",
"d=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)",
"b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)",
"c=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)",
"d=**(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(22,23)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -15488126/770887 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -2322020/117683 during the search for all slope function fixed points.
**